Real Estate Investment Performance Introduction Perform ance M easurem ent o N om inal, Realand ExcessReturns o M easuring RealEstate Risk o Sharpe’sRew ard to V ariability Index o Jensen’sIndex ofPerform ance G lobalPortfolio A llocations o CAPM o B lack-Litterm an Forw ard Looking A llocations Pension Funds
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Real Estate Investment Performance Introduction. Real Estate Investment Performance.
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Real Estate Investment PerformanceIntroduction
Performance Measurement
o Nominal, Real and Excess Returns
o Measuring Real Estate Risk
o Sharpe’s Reward to Variability Index
o Jensen’s Index of Performance
Global Portfolio Allocations
o CAPM
o Black-Litterman Forward Looking Allocations
Pension Funds
Real Estate Investment Performance
N o m i n a l R e t u r n s
T h e N o m i n a l H o l d i n g P e r i o d R e t u r n ( d u r i n g p e r i o d t ) , R t , i s :
w h e r e P t = e n d o f p e r i o d t p r i c e ; D t = p e r i o d t d i v i d e n d ;
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P P
PC a p i t a l g a i n y i e l d
D
PD i v i d e n d y i e l d
t t
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Real Estate Investment Performance
R e a l R e t u r n
T h e r e a l r e t u r n , r , i s t h e i n f l a t i o n a d j u s t e d n o m i n a l r e t u r n .
w h e r e R = n o m i n a l h o l d i n g p e r i o d r e t u r nh = t h e i n f l a t i o n r a t e
T h e F i s h e r E f f e c t : ( 1 + R ) = ( 1 + r ) ( 1 + h )
o r R = h + r + r h
N o t e : r h i s v e r y s m a l l a n d i s f r e q u e n t l y o m i t t e d
rR
h
1
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Real Estate Investment Performance
Excess Return
The excess return (on an asset or a portfolio) is the portion of the nominal holding period return, R, in excess of the risk free rate of return. The risk free rate of return is usually measured by the return on T-bills, Rf.
Excess Return = R - Rf
Real Estate Investment Performance
C o m p u t i n g A v e r a g e R e t u r n s :A r i t h m e t i c v s G e o m e t r i c
T h e r e a r e ( a t l e a s t ) t w o w a y s t o c o m p u t e a n a v e r a g e r e t u r n .
L e t R t = t h e r e t u r n o n a n a s s e t i n p e r i o d t .
Real Estate Investment Performance Risk Adjusted Performance Indexes
Sharpe Index
The Sharpe Index, SI, evaluates investment performance using total risk:
j
fj RRSI
_ Where Rj = the mean return on portfolio j Rf = the risk free rate of interest (T-bill return) σj = the standard deviation of excess returns on portfolio j.
Real Estate Investment Performance
Equity REITs Russell 2000 S&P 500
Monthly: 1979-2006:10 0.204 0.130 0.153
Annual: 1979-2005 0.679 0.488 0.559
Annual: 1980-1989 0.754 0.423 0.713
Annual: 1990-1999 0.313 0.553 1.048
Sharpe's Index of Performance
Note: the risk-free rate is measured using the monthly average of short- term US Treasury Securities
Real Estate Investment Performance Risk Adjusted Performance Indexes
Jensen’s Index of Performance
Jensen’s Index evaluates performance using market risk. It is based on the Capital Asset Pricing Model (CAPM). CAPM states that, in equilibrium, the expected return on an asset (or portfolio of assets) is related to the risk-free rate of return and the return on the market portfolio:
Real Estate Investment Performance Risk Adjusted Performance Indexes
Jensen’s Index of Performance CAPM:
fmjfj R)R
~E(R)R
~E(
~
where Rj = the random rate of return on portfolio j ~
Rm = the random rate of return on the market Rf = the risk free rate of interest (T-bill return)
βj = the beta coefficient; the risk of the jth asset (or portfolio) relative to the market risk
fm R)R
~E( is the market price of risk
Real Estate Investment Performance Risk Adjusted Performance Indexes
Jensen’s Index of Performance
jtmtjjjt rr
Where r jt = the excess return on portfolio j
r mt = the excess return on the market
βj = the beta coefficient or systematic risk
of the jth asset or portfolio
αj = Jensen’s Index of Performance
εjt = the random error term with E(εjt) = 0
Real Estate Investment Performance Risk Adjusted Performance Indexes
Jensen’s Index of Performance
A positive alpha indicates a superior performance of the investment fund relative to an unmanaged portfolio of similar market risk. A negative alpha indicates an inferior performance of the investment fund relative to an unmanaged portfolio of similar market risk.
Dependent Variable: Equity REITs Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.11011 0.11011 97.62 <.0001 Error 332 0.37449 0.00113 Corrected Total 333 0.48460 Root MSE 0.03359 R-Square 0.2272 Dependent Mean 0.00777 Adj R-Sq 0.2249 Coeff Var 432.14776 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 0.00500 0.00186 2.69 0.0075 SP500 SP500 1 0.42535 0.04305 9.88 <.0001
Dependent Variable: Russell 2000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.65491 0.65491 584.96 <.0001 Error 332 0.37170 0.00112 Corrected Total 333 1.02661 Root MSE 0.03346 R-Square 0.6379 Dependent Mean 0.00722 Adj R-Sq 0.6368 Coeff Var 463.70331 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 0.00045211 0.00185 0.24 0.8073 SP500 SP500 1 1.03733 0.04289 24.19 <.0001
Real Estate Investment Performance Portfolio Diversification
Portfolio: group of assets such as stocks and bonds held by an investor. Portfolio weight: the percentage of the portfolio’s total value in a particular asset. Let E{Ri} denote the expected return on asset i for i = 1,.....,N and wi denote the percentage of holdings invested in asset i. Let RP be the return on the portfolio. The expected portfolio return, E{RP}, is: E{RP} = w1E{R1} + w2 E{R2} + ... + wN E{RN}
Real Estate Investment Performance Portfolio Diversification
T h e v a r i a n c e o f t h e p o r t f o l i o r e t u r n i s :
N o t e t h e p o r t f o l i o v a r i a n c e i s n o t s i m p l y a w e i g h t e d a v e r a g e o ft h e i n d i v i d u a l a s s e t r e t u r n v a r i a n c e s .
A n d t h e s t a n d a r d d e v i a t i o n o f t h e p o r t f o l i o i s :
S t D e v { R P } =
V a r R P w V a r R w w C o v R Rii
N
i ij i
N
i
N
j i j{ } { } { , } 2
1 1
2
V a r R P{ }
Efficient frontier with and without REITsStocks, bonds, T-bills, and REITs 1972 – 2005
Source: www.nareit.com
Potential to reduce risk and increase returnStock and bond investors, 1972-2005
Source: www.nareit.com
Potential to reduce risk and increase returnFixed-income investors, 1972-2005
Top 1,000 plan assets grew 8.4% to about $6.5 trillion o Doubled since 1996 o Defined contribution plans grew 9.5% o Defined benefit plans grew 8%
Allocations for top 1000 plans o 43.7% in domestic equity, down 1.6 percentage points o 25.4% in domestic fixed income, up 0.5 percentage points o 16.8% in international equity, unchanged o 1.2% in international fixed income, unchanged o 3.9% in real estate equity, up 0.2% o 0.3% in mortgages, down 0.3% o 3.5% ‘other’